Question

A milkman purchases 10 litres of milk at Rs. 7 per litre and forms a mixture by adding freely available water which constitutes 16.66% of the mixture. Later on, he replaced the mixture by some freely available water and thus the ratio of milk is to water is 2:1. He then sold the new mixture at cost price of milk and replaced the amount of mixture at twice the cost of milk then what is the profit percentage?

• A. 68%
• B. 34%
• C. 40%
• D. None of these

Answer 1

The correct option is A 68%

Note: First of all the price of milk does not matter. You can assume any convenient price. Besides it instead of 10 litres of milk, you can consider 100 litres of milk to avoid calculations in decimal. Now, since water is 16.66% in the mixture of milk, therefore with 100 l pure milk 20 l water is added. Again note that in replacement method the quantity of mixture does not increase except to the variation in the ratio of contents.
Again by replacement formula
$\frac{80}{120}=\frac{100}{120}(1-\frac{K}{120})\Rightarrow K=24l$
Thus he replaces 24 l of the mixture with water. (Note the required ratio of milk is to water is 2: 1. It means in 3 l of new mixture, there will be 1 l of water)
Thus if the price of the new mixture is Rs.1, then the price of the replaced mixture be Rs. 2.
Therefore, total $SP=120\times 1+24\times 2=168$
and $CP=100\times 1=100$
$\therefore$ $Profit\%=68\%$